Have an answer to each box to correctly complete the derivation of a formula for the area of a sector of a circle.

Suppose a sector of a circle with radius r has a central angle of  θ

. Since a sector is a fraction of a __________ circle, the ratio of a sector's area A to the circle's area is equal to the ratio of the central angle to the measure of a full rotation of the circle. A full rotation of a circle is  2π  radians. This proportion can be written as  A/πr2=_____________ Multiply both sides by  πr2  and simplify to get ________, where  θ  is the measure of the central angle of the sector and r is the radius of the circle.


Please help guys, you rock! I am not very good at proofs haha

wertyusop  Jan 19, 2018
edited by wertyusop  Jan 19, 2018

2+0 Answers


The stuff in red goes into each respective blank




 Note, werty.....that the second blank can be interpreted like this :


A /  [ pi r^2 ]   =   θ / [ 2pi ]           [ multiply both sides by pi r^2  ]


A  =  [ θ / 2 ]  r^2  =    (1/2)r^2 θ



cool cool cool

CPhill  Jan 19, 2018
edited by CPhill  Jan 20, 2018

Awesome, that does look right. Thanks for explaing and making it easier CPhill. laugh

wertyusop  Jan 19, 2018

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